Shred the cheeses. Rub inside of a 4-quart fondue pot with the cut sides of garlic, add wine or cider to pot and bring just to a simmer over medium low heat on your stovetop.

Stir together cornstarch and kirsch in a cup.

Gradually add the cheese to the pot and cook, stirring constantly in a zigzag pattern to prevent cheese from balling up, until cheese is just melted and creamy (do not let it boil). Stir cornstarch mixture again and add it to the fondue. Continue to simmer, stirring the fondue until it becomes thick, 5 to 8 minutes.

Transfer to fondue pot set over a flame and serve with your accompaniments for dipping.